Approximate strong separation with application in fractional graph coloring and preemptive scheduling

Abstract

In this paper we show that approximation algorithms for the weighted independent set and s-dimensional knapsack problem with ratio a can be turned into approximation algorithms with the same ratio for fractional weighted graph coloring and preemptive resource constrained scheduling. In order to obtain these results, we generalize known results by Grötschel, Lovasz and Schrijver on separation, non-emptiness test, optimization and violation in the direction of approximability.